There's a way to find every single rational root for some of the polynomials:

step one:

we have the polynomial a0+a1*x+a2*x2+a3*x3+........+an*xn=0. We need to multiply the polynomial by a number in a way that all coefficients will be whole numbers. Sometimes we cant do it. sometimes we can.

step two:

find all of the whole divisors of an and a0 (including the negative divisors). lets call the set of the divisors of a0 A and the set of the divisors of an B. there are k divisors in A and m divisors in B.

Every rational root of the polynomial=Ai/Bj, 0 i is a member of A and B j is a member of B, meaning every rational root can be expressed using one divisor from A divided by one divisor from B).

step three:

Check for every two divisors (one from A and one from B) if Ai/Bj is a root. after a finite amount of time (unless your calculator is broken) you'll have every rational root of the polynomial.

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